(Solved): \( \ln (a)-\ln (b)=\ln (a-b) \) for all positive real numbers \( a \) and \( b \). True. Take \( a= ...

\( \ln (a)-\ln (b)=\ln (a-b) \) for all positive real numbers \( a \) and \( b \). True. Take \( a=4 \) and \( b=2 \). Then \( \ln (a)-\ln (b)=\ln (4)-\ln (2)=\ln \left(\frac{4}{2}\right)=\ln (2) \). And \( \ln (a-b)=\ln (4-2)=\ln (2) \). True. This is one of the Laws of Logarithms. False. \( \ln (a-b)=\ln (a)-\ln (b) \) only for negative real numbers \( a \) and \( b \). False. \( \ln (a-b)=\ln (a)-\ln (b) \) only for positive real numbers \( a>b \). False. Take \( a=2 \) and \( b=1 \). Then \( \ln (a)-\ln (b)=\ln (2)-\ln (1)=\ln (2)-0=\ln (2) \). But \( \ln (a-b)=\ln (2-1)=\ln (1)=0 \).